Fake user in UV Editor. What is it for?
Why is it there?

It's basically because of Object Oriented Programming. In OOP, for matter of coding efficiency, you tend to create sub-classes of classes to re-use some or all of their properties. Since Image Textures and the Render Result slot derive from the same parent class, they inherit all those properties. The fake user property is already part of the parent, so there is actually no way for the child class NOT to have it.

Keep in mind that you're not setting a fake user on the render result itself, but on the datablock displaying it. Think of it as a container. This container inherits from ID, which holds the use_fake_user property.

How could it make sense?

Well, there is a case where you can make use of it. The Render Result slot isn't just the pixels, it's a whole datablock with properties attatched. One of those properties is a Render Slot name per slot. If you set the fake user, names you give to render slots will be preserved upon file save. In the example below, I created a render slot named Demo. When saving and reloading, the named slot is kept. If you don't set a fake user, you lose that data.